The Inductive (Scientific) Method

Historical Development:

Not everyone from 300 B.C. to 1600 A.D. was willing to bow to the
authority of Aristotle.
Many of Aristotle's arguments were faulty, but where did he go wrong,
and what was the right way to proceed?

Galileo Galilei

Sir Francis Bacon (1561 - 1626)

Tycho Brahe (1546 - 1601)

About 1600 A.D., it became apparent to several people - Galileo
Galilei in Italy, Francis
Bacon in England, Tycho
Brahe in Denmark, and others - that there were no subtle logical
errors in Aristotle's use of the deductive
method. The problem was that the deductive method, while wildly
successful in mathematics, did not fit well with scientific
investigations of nature.

In order to use the deductive method, you need to start with
axioms - simple true statements about the way the world works. Then
you use these axioms to build your logical system of nature. If your
axioms are true, everything that follows will be true, but Galileo
and his contemporaries realized that the problem was that it was
enormously difficult to determine "simple true statements about the
way the world works". In fact, they realized that it should be the
goal of science -
not the starting place - to determine what
the "simple true statements about the way the world works" really
are!

Since 1600, the inductive method has been incredibly successful in
investigating nature - surely far more successful than its
originators could have imagined. The inductive method of
investigation has become so entrenched in science that it is often
referred to as the scientific method.

Inductive vs. Deductive
Method

The inductive method (usually called the scientific method) is the
deductive method "turned upside down". The deductive method starts
with a few true statements (axioms) with the goal of proving many
true statements (theorems) that logically follow from them. The
inductive method starts with many observations
of nature, with the goal of finding a few, powerful statements about
how nature works (laws and theories).

In the deductive method, logic is the authority. If a statement
follows logically from the axioms of the system, it must be true. In
the scientific method, observation of nature is the authority. If an
idea conflicts with what happens in nature, the idea must be changed
or abandoned.

Here is a diagram that attempts to depict the scientific
(inductive) method. It is oversimplified and incomplete, but...

Is Science Entirely Inductive?

On the previous page, you learned that although mathematics is
deductive in nature - that is, logical proof is the only
acceptable evidence of truth - the process of mathematics is
not entirely deductive. It is also true that although science is
inductive by nature - observations are the only acceptable evidence
of truth - the process of science can be deductive!

In particular, physicists make extensive use of mathematics as a
powerful theoretical tool. Theoretical physicists often construct
theories as "mathematical models"
deductively, starting with assumptions about the inner workings of
stars or atoms, for instance, and then working out the mathematical
consequences of their assumptions. An essential difference between a
mathematician and a theoretical physicist is that the physicist uses
mathematics as a reasoning tool. The success of the mathematical
model depends on how well its results agree with observations of
nature - if they do not agree the physicist knows that this means
that her assumptions - not the observations - need to be
adjusted.